Finite Group Databasebeta

← #21450104

Subgroups — #21450104

Order 7808.

512 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519734C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839704C211yesmaximal, characteristic, complemented
4#16839703C211yesmaximal, characteristic, complemented
5#16839696C211yesmaximal, characteristic, complemented
6#16839695C211yesmaximal, characteristic, complemented
7#16839647C211yesmaximal, characteristic, complemented
8#16839646C211yesmaximal, characteristic, complemented
9#16839643C211yesmaximal, characteristic, complemented
10#16839636C211yesmaximal, characteristic
11#16839633C211yesmaximal, characteristic
12#16839624C211yesmaximal, characteristic
13#16839624C211yesmaximal, characteristic
14#16839624C211yesmaximal, characteristic
15C61×#387C211yesmaximal, characteristic, complemented
16C22×C4×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519734—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C4⋊C4×D61—24no—
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C42×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C23×D61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61D414yes—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—22no—
79C42×C61—22no—
80#11758198—22no—
81#11758198—22no—
82#11758198—22no—
83#11758198—22no—
84C4⋊Dic61—22no—
85C4⋊Dic61—22no—
86#11758196—22no—
87#11758196—22no—
88#11758196—22no—
89#11758196—22no—
90#11758196—22no—
91#11758196—22no—
92C4×Dic61—22no—
93C23×C61C2411yescharacteristic
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—21no—
98C22×D61C2×D412yes—
99C22×D61#4112yes—
100C22×D61#4112yes—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61C2×D412yes—
121C2×C4×C61#4112yes—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D412yes—
142C2×Dic61#4112yes—
143C4×D61—28no—
144C4×D61—28no—
145C4×D61—44no—
146C22×C61C22×D411yescharacteristic
147C22×C61C2×#4111yescharacteristic
148C22×C61C2×#4111yescharacteristic
149C22×C61C2×#4111yescharacteristic
150C22×C61C2×#4111yescharacteristic
151C22×C612−1+411yescharacteristic
152C22×C612−1+411yescharacteristic
153C2×D61—22no—
154C2×D61—22no—
155C2×D61—22no—
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61#12314yes—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167Dic61—22no—
168Dic61—22no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#2484—611nomaximal, Sylow
175C2×C61C2×#12311yescharacteristic
176C2×C61#52511yescharacteristic
177C2×C61#53611yescharacteristic
178C2×C61#55211yescharacteristic
179C2×C61#55211yescharacteristic
180C2×C61#55211yescharacteristic
181C2×C61#55211yescharacteristic
182D61—24no—
183C2×#117—611no—
184C22×C4⋊C4—611no—
185#400—611no—
186#400—611no—
187#398—611no—
188#398—611no—
189#387—611no—
190#387—611no—
191#387—611no—
192#387D6111yescharacteristic, complemented
193#385—611no—
194#385—611no—
195#381—611no—
196#381—611no—
197#381—611no—
198C61#248411yescharacteristic, complemented, Sylow
199C23×C4—611no—
200C23×C4—611no—
201C23×C4—611no—
202#117—1224no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1224no—
212C2×C4⋊C4C2×D6111yescharacteristic
213C2×C4⋊C4C2×D6111yescharacteristic
214C2×C22⋊C4—611no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C42—611no—
219C2×C42C2×D6111yescharacteristic
220#95—611no—
221#95—611no—
222#95—611no—
223#95—611no—
224#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95C2×D6111yescharacteristic
233#95C2×D6111yescharacteristic
234#95C2×D6111yescharacteristic
235#95C2×D6111yescharacteristic
236C24—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—614no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C22×C4C22×D6111yescharacteristic
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259C22×C4C22×D6111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—1222no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—1222no—
270C22⋊C4—1222no—
271C22⋊C4—1222no—
272C22⋊C4—1222no—
273C22⋊C4—1222no—
274C42—22no—
275C42—1222no—
276C23—612no—
277C23—612no—
278C23—612no—
279C23—1221no—
280C23—1221no—
281C23—1221no—
282C23—1221no—
283C23C23×D6111yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—612no—
304C2×C4—612no—
305C2×C4—1228no—
306C2×C4—1228no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—2444no—
327C2×C4#1175822212yes—
328C2×C4D4×D6112yes—
329C22—614no—
330C22—1222no—
331C22—1222no—
332C22—1222no—
333C22—1222no—
334C22—1222no—
335C22—1222no—
336C22C2×D4×D6111yescharacteristic
337C22#41×D6111yescharacteristic
338C22#41×D6111yescharacteristic
339C22#41×D6111yescharacteristic
340C22C2×#1175822211yescharacteristic
341C22#1451982411yescharacteristic
342C22#1451982511yescharacteristic
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—1222no—
351C4—1222no—
352C4—2441no—
353C4—2441no—
354C4—2441no—
355C4—2441no—
356C4—2441no—
357C2—1224no—
358C2#123×D6111yescharacteristic
359C2#1684027111yescharacteristic
360C2#1684033511yescharacteristic
361C2#1684044411yescharacteristic
362C2#1684044811yescharacteristic
363C2#1684045111yescharacteristic
364C2#1684045311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#387C2
hypercenter#387D61
hypocenterC61#2484
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #16839704C2semidirect
4. #16839703C2semidirect
5. #16839696C2semidirect
6. #16839695C2semidirect
7. #16839647C2semidirect
8. #16839646C2semidirect
9. #16839643C2semidirect
15. C61×#387C2semidirect
192. #387D61semidirect
198. C61#2484semidirect